Lyapunov Spectra of Periodic Orbits for a Many-Particle System

The Lyapunov spectrum corresponding to a periodic orbit for a two dimensional many particle system with hard core interactions is discussed. Noting that the matrix to describe the tangent space dynamics has the block cyclic structure, the calculation of the Lyapunov spectrum is attributed to the eigenvalue problem of 16× 16 reduced matrices regardless of the number of particles. We show that there is the thermodynamic limit of the Lyapunov spectrum in this periodic orbit. The Lyapunov spectrum has a step structure, which is explained by using symmetries of the reduced matrices.